A tiny but horrible alien is standing at the top of the Eiffel Tower (which is $324$ meters tall) and threatening to destroy the city of Paris! A Men In Black agent is standing at ground level, $54$ meters across the Eiffel square, aiming his laser gun at the alien. At what angle, in degrees, should the agent shoot his laser gun? Round your final answer to the nearest tenth.
Answer: The strategy Model the situation as a right triangle. Determine the appropriate trigonometric ratio in order to find the missing angle. Form an equation and solve for the missing angle. Calculate the final result and round. Modeling as a right triangle This situation can be modeled by the following right triangle. The height is $324\text{ m}$ and the base is $54\text{ m}$. We are asked to find the angle at which the agent should shoot, which is the angle on the left. $324$ $54$ $?$ Determining the appropriate trigonometric ratio We are given the side ${\text{opposite}}$ to the missing angle and the side ${\text{adjacent}}$ to the missing angle. The appropriate trigonometric ratio is therefore the $\text{tangent}$. Forming an equation and solving Denoting the missing angle by $\theta$, we obtain the equation $\tan(\theta)=\dfrac{324}{54}$. Solving the equation, we get $\theta=\tan^{-1}\left(\dfrac{324}{54}\right)$. Evaluating this result in the calculator and rounding to the nearest tenth, we get $\theta=80.5^\circ$. Summary The agent should shoot his laser at an angle of $80.5^\circ$.